The Republican presidential hopefuls got the free-for-all debate they had asked for Tuesday, interrupting each other, brushing aside time limits and loudly talking over their opponents as the moderators just looked on.

“We wanted to make sure the candidates had their say,” said Neil Cavuto of Fox Business News, one of the moderators of the two-hour debate from Milwaukee.

While the eight candidates on the stage may not have shed a lot of new light on their presidential campaigns or their pet issues, there was plenty of heat in a showdown that often sounded more like a back-alley brawl than a reasoned exchange of opinion.

The verbal fisticuffs started about 10 minutes into the debate, when Donald Trump talked about his plan to deport everyone who is in the country illegally.

“We will have a wall and it will work,” he said. “We’re a country of laws. We either have a country or we don’t have a country.”

Ohio Gov. John Kasich immediately jumped in to say that there is no way the country is going to pull 11 million people from their homes and ship them away.

“You know they can’t do that,” he told Trump. “It’s a silly argument.”

“I built a company worth billions and billions of dollars,” replied the clearly irritated Trump. “I don’t have to listen to this man.”

Family tax credit

Later it was Florida Sen. Marco Rubio and Kentucky Sen. Rand Paul who scrapped after Rubio talked how important it is to spend about $1 trillion to boost the family tax credit for children.

“The most important job I’ll have is being a parent,” he said, arguing that strong families are needed to raise children with strong values. “Yes, I have a child tax credit increase and I’m proud of it.”

But Paul argued that Rubio’s proposed tax credit and his call for a $1 trillion boost in military spending didn’t match the rest of his call for a smaller government.

“Marco, Marco, Marco,” Paul said, chidingly. “You can’t be a conservative if you keep promoting new programs that you’re not going to pay for.”

National defense brought the next sharp exchange, with Trump standing up for Russian President Vladimir Putin, whom he said he met while waiting for an appearance on “60 Minutes.”

“If Putin wants to go in and knock hell out of ISIS (in Syria and Iraq), I’m for it 100 percent,” he said. “We have to get smart. We can’t continue to be the policeman of the world.”

Former Florida Gov. Jeb Bush, who once again struggled to insert himself into the debate, shot back that “Donald is 100 percent wrong” and is treating the problems of the Mideast “like a board game, like playing Monopoly. ... We have a role to play in this.”

Businesswoman Carly Fiorina took a jab at Trump, saying that she has met Putin and “not in a greenroom for a show.” She said she wouldn’t speak to the Russian leader but instead would establish a no-fly zone in and around Syria and Iraq, rebuild the Sixth Fleet, schedule visible military exercises in the Baltics and “put a few thousand more troops in Germany, not to start a war, but to let him know we mean business.”

That brought Paul in, saying the candidates need to realize that Russian planes are flying combat missions at the invitation of the Iraqi government.

Setting up a no-fly zone “means we’re going to shoot down Russian planes,” he said. “If we do that, get ready to send your sons and daughters to a new war in Iraq.”

Cavuto, Fox Business News anchor Maria Bartiromo and Gerald Baker, editor in chief of the Wall Street Journal, spent most of the evening on the sidelines, asking their questions and then stepping back, only occasionally asking follow-up questions and either unwilling or unable to break into the sharp exchanges among the candidates. The bell calling time on a candidate was treated as merely a suggestion.

It was in sharp contrast to last month’s CNBC-sponsored debate, where the candidates and GOP loyalists complained loudly about both what they said were “gotcha” questions and a format that often cut a candidate’s response short.

It wasn’t all a chin-to-chin battle. Ben Carson, for example, got a chance to talk about the rash of media questions about the accuracy of the life story he tells.

“Thank you for not asking me what I said in 10th grade,” he said, arguing that his remarks about being offered a scholarship to West Point had been misinterpreted.

“I don’t have any problems about being vetted; we should vet all candidates,” he said. “I do have a problem about being lied about and putting that out as truth.”

Call for a flat tax

Texas Sen. Ted Cruz also put out details of his economic plan, which calls for a 10 percent flat tax on individuals, a 16 percent flat tax on businesses and the elimination of the Internal Revenue Service and the departments of commerce, energy, housing and urban development.

He also said that he would refuse to bail out any failing banks, regardless of their size, and that changes are needed in the Federal Reserve.

Earlier in the evening, there was more than a whiff of desperation during the hour-long undercard debate, where candidates just a couple of percentage points above invisibility in the polls tried to do something — anything — to make their mark with GOP voters.

New Jersey Gov. Chris Christie, former Arkansas Gov. Mike Huckabee, Louisiana Gov. Bobby Jindal and former Pennsylvania Sen. Rick Santorum slammed each other and the Democrats in an effort to vault themselves into the pack of front-runners.

John Wildermuth is a San Francisco Chronicle staff writer. E-mail: jwildermuth@